How do I connect my Apple TV to my WiFi without a remote?

No. The Apple TV and the iPhone need to be already connected to the same Wifi network to setup the Apple TV Remote App, or the Apple Tv Remote Widget on control center (for 4th and 4K apple tvs).

If you have not set up the remote app in older versions of Apple TV before hand, you cannot set it up without the physical remote.

You can of course buy a new Remote:

Buy Apple Remote (Silver) - Apple

Buy Siri Remote (4th and 4K) - Apple

if the ATV is logged into your Apple ID and has a wi-fi or cabled connection you can use the ATV app for an iOS device as the remote. I'm not entirely sure but I think it will work without having to pair it but they do need to be on the same network to see each other.

https://itunes.apple.com/us/app/apple-tv-remote/id1096834193?mt=8